Its very likely that all the neoprene parts, the metering diaphragm and the pump/check valve "gasket", are stiffened up from the exposure to gas and time. I have found these parts to last about 2-3 years using pump gas with ethanol and somewhat longer on ethanol-free gas or avgas. The carb cannot respond to atmospheric pressure if the diaphragm is bad and it won't pump if the pump/check valve is bad. Look for the carb part number stamped on the body and order a rebuild kit from Walbro or a Walbro parts vendor. These carbs are very simple and not difficult to work on, the exception being a tiny spring under the metering lever on the diaphragm side of the carb. Don't remove the metering lever unless absolutely necessary. The very small low speed orifices just behind the throttle plate are likely stopped up as well. These are difficult to clean without removing a small aluminum Welsh plug under the diaphragm and they are easy to damage if care is not taken. I use an ultrasonic cleaner to open up these small passages and it can take awhile even with at that. You can check to see if these passages are open by blowing some carb cleaner into the low speed needle hole. Be careful not to blow it into your eyes or face. Depending on the carb there will be several of these small holes visible behind the throttle plate where it seats when closed.
Andy
Andy's Model Engine Repair
www.modelenginerepair.com